# Question #507e9

Sep 27, 2017

$\left(3 x + 8\right) \left(x - 1\right) = 0$

i.e. $x = - 2 \frac{2}{3}$ or $x = 1$

#### Explanation:

$- 3 {x}^{2} - 5 x + 8 = 0$

$3 {x}^{2} + 5 x - 8 = 0$

The product of coefficient of first and last term is $3 \setminus \times - 8 = - 24$

So we need to find two such numbers whose sum is equal to the middle term $5$and product is $- 24$.

$8$ and $- 3$ are two numbers which sum up to $5$and their product is $- 24$. Therefore we write the equation as:

$3 {x}^{2} - 3 x + 8 x - 8 = 0$

$3 x \left(x - 1\right) + 8 \left(x - 1\right) = 0$

$\left(3 x + 8\right) \left(x - 1\right) = 0$

Therefore:
$\left(3 x + 8\right) = 0$ i.e. $x = - \frac{8}{3}$ = $2 \frac{2}{3}$
or
$\left(x - 1\right) = 0$ i.e. $x = 1$

Answer : $x = - 2 \frac{2}{3}$ or $x = 1$